def gto2tuck(w,cf,x):
n = len(x)
r = len(cf)
k=0
for alpha in xrange(r):
k += len(w[alpha].prims)
U1 = np.zeros((n,k*r))
U2 = np.zeros((n,k*r))
U3 = np.zeros((n,k*r))
c = np.zeros(k*r)
nG = 0
for alpha in xrange(r):
for beta in xrange(len(w[alpha].prims)):
prim = w[alpha].prims[beta]
i,j,k = prim.powers
x0,y0,z0 = prim.origin
#print [x0,y0,z0]
U1[:,beta + nG] = pow(x-x0,i)*np.exp(-prim.exp*(x-x0)**2)
U2[:,beta + nG] = pow(x-y0,j)*np.exp(-prim.exp*(x-y0)**2)
U3[:,beta + nG] = pow(x-z0,k)*np.exp(-prim.exp*(x-z0)**2)
c[beta + nG] = w[alpha].norm*prim.norm*prim.coef*cf[alpha]
nG += len(w[alpha].prims)
return tuck.can2tuck(c,U1,U2,U3)
def poisson(F, mu, N, h, eps, r_add = 4, solver='Fourier'): # check N+1
#solves (-\Delta + mu) = F with F.shape = N \times N \times N
U1_L = np.ones((F.n[0], 4), dtype = np.float64)
U2_L = U1_L.copy()
U3_L = U1_L.copy()
if solver=='Fourier':
U1_L[:, 0] = 4. * np.sin(1./(N+1)*(np.array(range(F.n[0]))+1)*pi/2)**2 / h**2
elif solver=='spectral':
U1_L[:, 0] = np.pi**2 * (np.array(range(F.n[0]))+1)**2
else:
raise Exception('Incorrect poisson solver name')
U1_L[:, 3] = mu * U1_L[:, 3].copy()
U2_L[:, 1] = U1_L[:, 0].copy()
U3_L[:, 2] = U1_L[:, 0].copy()
g = np.ones(F.n[0], dtype = np.float64)
L = tuck.can2tuck(g, U1_L, U2_L, U3_L)
#L = tuck.round(L, 1e-14)
f = tuck.dst(F)
frac = tuck.cross.multifun([f, L], eps, lambda (a, b): a/b, r_add = r_add)
sol = tuck.dst(frac)
return sol
def newton(x, eps, ind):
# galerkin tensor for convolution as a hartree potential
if ind == 6:
a, b, r = -15., 10, 80
elif ind == 8:
a, b, r = -20., 15, 145
elif ind == 10:
a, b, r = -25., 20, 220
elif ind == 12:
a, b, r = -30., 25, 320
else:
raise Exception("wrong ind parameter")
N = x.shape
hr = (b-a)/(r - 1)
h = x[1]-x[0]
s = np.array(range(r), dtype = np.complex128)
s = a + hr * (s - 1)
w = np.zeros(r, dtype = np.complex128)
for alpha in xrange(r):
w[alpha] = 2*hr * np.exp(s[alpha]) / np.sqrt(pi)
w[0] = w[0]/2
w[r-1] = w[r-1]/2
U = np.zeros((N[0], r), dtype = np.complex128)
for alpha in xrange(r):
U[:, alpha] = ( func_int(x-h/2, x[0]-h/2, np.exp(2*s[alpha])) -
func_int(x+h/2, x[0]-h/2, np.exp(2*s[alpha])) +
func_int(x+h/2, x[0]+h/2, np.exp(2*s[alpha])) -
func_int(x-h/2, x[0]+h/2, np.exp(2*s[alpha])) )
newton = tuck.can2tuck(w, U, U, U)
newton = tuck.round(newton, eps)
return (1./h**3) * newton
def newton(x, eps, ind):
# galerkin tensor for convolution as a hartree potential
if ind == 6:
a, b, r = -15., 10, 80
elif ind == 8:
a, b, r = -20., 15, 145
elif ind == 10:
a, b, r = -25., 20, 220
elif ind == 12:
a, b, r = -30., 25, 320
else:
raise Exception("wrong ind parameter")
N = x.shape
hr = (b - a) / (r - 1)
h = x[1] - x[0]
s = np.array(range(r), dtype=np.complex128)
s = a + hr * (s - 1)
w = np.zeros(r, dtype=np.complex128)
for alpha in xrange(r):
w[alpha] = 2 * hr * np.exp(s[alpha]) / np.sqrt(pi)
w[0] = w[0] / 2
w[r - 1] = w[r - 1] / 2
U = np.zeros((N[0], r), dtype=np.complex128)
for alpha in xrange(r):
U[:,
alpha] = (func_int(x - h / 2, x[0] - h / 2, np.exp(2 * s[alpha])) -
func_int(x + h / 2, x[0] - h / 2, np.exp(2 * s[alpha])) +
func_int(x + h / 2, x[0] + h / 2, np.exp(2 * s[alpha])) -
func_int(x - h / 2, x[0] + h / 2, np.exp(2 * s[alpha])))
newton = tuck.can2tuck(w, U, U, U)
newton = tuck.round(newton, eps)
return (1. / h**3) * newton
def coulomb(x, vec, ind, eps, beta=1.0): # 1/|r-vec|**beta in Tucker format
if ind == 6:
a, b, r = -15., 10, 80
elif ind == 8:
a, b, r = -20., 15, 145
elif ind == 10:
a, b, r = -25., 20, 220
elif ind == 12:
a, b, r = -30., 25, 320
else:
raise Exception("wrong ind parameter")
N = x.shape
h = (b-a)/(r - 1)
s = np.array(range(r))
s = a + h * (s - 1)
w = np.zeros(r, dtype = np.float64)
for alpha in xrange(r):
w[alpha] = 2*h * np.exp(beta*s[alpha]) / gamma(beta/2)
w[0] = w[0]/2
w[r-1] = w[r-1]/2
U1 = np.zeros((N[0], r), dtype=np.float64)
U2 = np.zeros((N[0], r), dtype=np.float64)
U3 = np.zeros((N[0], r), dtype=np.float64)
for alpha in xrange(r):
U1[:, alpha] = np.exp(-(x-vec[0])**2 * np.exp(2*s[alpha]))
U2[:, alpha] = np.exp(-(x-vec[1])**2 * np.exp(2*s[alpha]))
U3[:, alpha] = np.exp(-(x-vec[2])**2 * np.exp(2*s[alpha]))
newton = tuck.can2tuck(w, U1, U2, U3)
newton = tuck.round(newton, eps)
return newton
def coulomb(x, vec, ind, eps, beta=1.0): # 1/|r-vec|**beta in Tucker format
if ind == 6:
a, b, r = -15., 10, 80
elif ind == 8:
a, b, r = -20., 15, 145
elif ind == 10:
a, b, r = -25., 20, 220
elif ind == 12:
a, b, r = -30., 25, 320
else:
raise Exception("wrong ind parameter")
N = x.shape
h = (b - a) / (r - 1)
s = np.array(range(r))
s = a + h * (s - 1)
w = np.zeros(r, dtype=np.float64)
for alpha in xrange(r):
w[alpha] = 2 * h * np.exp(beta * s[alpha]) / gamma(beta / 2)
w[0] = w[0] / 2
w[r - 1] = w[r - 1] / 2
U1 = np.zeros((N[0], r), dtype=np.float64)
U2 = np.zeros((N[0], r), dtype=np.float64)
U3 = np.zeros((N[0], r), dtype=np.float64)
for alpha in xrange(r):
U1[:, alpha] = np.exp(-(x - vec[0])**2 * np.exp(2 * s[alpha]))
U2[:, alpha] = np.exp(-(x - vec[1])**2 * np.exp(2 * s[alpha]))
U3[:, alpha] = np.exp(-(x - vec[2])**2 * np.exp(2 * s[alpha]))
newton = tuck.can2tuck(w, U1, U2, U3)
newton = tuck.round(newton, eps)
return newton